Average Error: 17.1 → 0.4
Time: 10.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r157489 = J;
        double r157490 = l;
        double r157491 = exp(r157490);
        double r157492 = -r157490;
        double r157493 = exp(r157492);
        double r157494 = r157491 - r157493;
        double r157495 = r157489 * r157494;
        double r157496 = K;
        double r157497 = 2.0;
        double r157498 = r157496 / r157497;
        double r157499 = cos(r157498);
        double r157500 = r157495 * r157499;
        double r157501 = U;
        double r157502 = r157500 + r157501;
        return r157502;
}
↓
double f(double J, double l, double K, double U) {
        double r157503 = J;
        double r157504 = 0.3333333333333333;
        double r157505 = l;
        double r157506 = 3.0;
        double r157507 = pow(r157505, r157506);
        double r157508 = r157504 * r157507;
        double r157509 = 0.016666666666666666;
        double r157510 = cbrt(r157505);
        double r157511 = r157510 * r157510;
        double r157512 = 5.0;
        double r157513 = pow(r157511, r157512);
        double r157514 = r157509 * r157513;
        double r157515 = pow(r157510, r157512);
        double r157516 = cbrt(r157515);
        double r157517 = r157516 * r157516;
        double r157518 = cbrt(r157517);
        double r157519 = cbrt(r157516);
        double r157520 = r157518 * r157519;
        double r157521 = r157520 * r157516;
        double r157522 = r157521 * r157516;
        double r157523 = r157514 * r157522;
        double r157524 = 2.0;
        double r157525 = r157524 * r157505;
        double r157526 = r157523 + r157525;
        double r157527 = r157508 + r157526;
        double r157528 = r157503 * r157527;
        double r157529 = K;
        double r157530 = 2.0;
        double r157531 = r157529 / r157530;
        double r157532 = cos(r157531);
        double r157533 = r157528 * r157532;
        double r157534 = U;
        double r157535 = r157533 + r157534;
        return r157535;
}

Error

Bits error versus J

Bits error versus l

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.1

    \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  2. Taylor expanded around 0 0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\color{blue}{\left(\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}\right)}}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  5. Applied unpow-prod-down0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot \color{blue}{\left({\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5} \cdot {\left(\sqrt[3]{\ell}\right)}^{5}\right)} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  6. Applied associate-*r*0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\color{blue}{\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot {\left(\sqrt[3]{\ell}\right)}^{5}} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right)} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot \left(\left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  11. Applied cbrt-prod0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot \left(\left(\color{blue}{\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}}\right)} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  12. Final simplification0.4

    \[\leadsto \left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\left(\frac{1}{60} \cdot {\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)}^{5}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}} \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\ell}\right)}^{5}}\right) + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Reproduce

herbie shell --seed 2020089 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))